Tag Archives: Building Foundations

In my last post, I talked about the connection between decomposing numbers and place value.

Understanding how numbers can be decomposed into parts lays the foundation for breaking apart numbers into specific groups. These specific groups could be anything, but for our numeration system they will be ten. You may want to check out the blog before reading on.

But decomposing also builds the foundation for addition. The concept of addition is apparent even when you look at the pictures and numbers above, you just need to add the symbols. Caution: You don’t want to have your students write number sentences too quickly. They need to talk about it and experience it first! Every time they take unifix cubes, beads, paper clips, or anything else that you have found for them to visualize decomposing, they are building a stronger foundation of number conservation. They need to internalize that numbers can be decomposed in lots of different ways and they are still the original number.

Students should use the student page after they have understanding of decomposing, so that they connect decomposing to the abstract number sentence. (Mathematical Practice 2-Reason abstractly and quantitatively.) If they use it too soon they will just give you answers and that just isn’t good enough. We need them to build mathematical knowledge!

Click to download a PDF of the sentence frame.

You may also want to decompose the number with multiple addends. Why? We want to give our students a variety of experiences that build a foundation and do not lead to misconceptions. We wouldn’t want students to think numbers could only be decomposed into two different parts. But that is exactly what we communicate non-verbally when it is the only experiences we give them.

Click to download a PDF of the sentence frame.

Here is one more idea for decomposing! It will even help your students subitize numbers.

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I hope that you have found these two blogs helpful in your journey of teaching. I would love to hear from you!